Nash's Nobel idea

When one billiard ball hits smack into an identical ball,
the first stops dead in its tracks and the second starts moving in
the same direction, and at the same speed, as the first was going.
This fact has been known since the beginning of time or at least sincepractically
as long agothe game of billiards was invented. Surely, you would
think, only a charlatan or a fool would take the trouble to express
this obvious fact as a mathematical formula and then have the nerve
to proclaim it as a fundamental scientific advance. Yet that is essentially
what Isaac Newton did when he formulated the conservation of momentum
as one of his three laws of physics. In fact, rather than being an
uninterpretable tangle of math hieroglyphics and Greek letters, a
fundamental scientific law is more often a suggestion that something
obvious but not previously recognized as worthy of attention actually
has far-reaching implications.

So it is with the idea of "Nash equilibrium" of a game,
for which Nash won the Nobel Prize in 1994. Economists use the word
"game" to refer to any situation in which people have to worry about
what one another are going to do. By an equilibrium, economists mean
a specification of what those people do and why they choose to do
it. Let's consider two brothers, Click and Clack, who live five miles
apart, connected only by a two-lane road with a footpath beside it.
Click and Clack each own a jalopy, and their lives revolve around
travelling up and down the road and waving at one another as they
pass. Click and Clack each have three choices: to drive on the right,
to drive on the left or to walk. Each would like to take a spin in
his jalopy if the other is going to make a compatible choice, but
would prefer to walk rather than to have a collision. Without being
connected by a telephone, they cannot coordinate their choices. This
is a game. What is going to happen, and why? That is, what will be
an equilibrium?

Back in the dark ages before Nash, economists used to
analyze this situation by supposing that Click and Clack would each
make a choice that offers the best insurance against the worst-case
choice by the other. If Click drives on the right, then the worst-case
choice by Clack would be to drive on the left when going in the opposite
direction. A collision would result. Similarly, Click would suffer
a collision with Clack if he chose to drive on the left and Click
made the worst-case choice of driving on the right. No matter which
choice Clack makes, though, all that happens to Click if he walks
to Clack's place is that the trip takes longer than he wisheshis
beloved jalopy is not wrecked. So, among the worst-case outcomes of
the choices that Click can make, his choice to walk will ensure the
best (or, at least, the least bad) of the lot. That is the prediction
that the dark-ages economist would make regarding Click's choice,
and by parallel reasoning the economist would also predict that Clack
would walk.

In reality, all over the world, there are drivers who do not explicitly
communicate with one another but who nevertheless enjoy their jalopies
because they expect not to get into collisions most of the time. Americans
may expect to keep safe by driving on the right while British drivers
expect to keep safe by driving on the left, but the fact that either convention
can work does not contradict the point: that people make choices by basing
their forecasts of benefits and costs on rational expectations of what
other people are going to donot on pessimistic conjectures about
worst-case outcomesand that the various people's expectations are
rational because the resulting choices make them mutually self-confirming.
This, in a nutshell, is Nash equilibrium. Simple, isn't it? But it does
explain all those cars being on the road, and much else besides, as the
deliberate reference to "rational expectations" ought to suggest.